Electrostatics and Riemann Surfaces

Spencer Tamagni; Costas Efthimiou

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arXiv · 2006.07149

Electrostatics and Riemann Surfaces

Spencer Tamagni·Costas Efthimiou

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Abstract

Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions when their argument is complex-valued. The underlying connections between these techniques and the theory of Riemann surfaces are also explained. Our goal is to provide students and instructors a quick reference article for an extraordinary topic that is not included in the standard books.

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Spencer Tamagni, Costas Efthimiou. 2020-06-04. Electrostatics and Riemann Surfaces. https://arxiv.org/abs/2006.07149

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